What is the value of cos(3((3pi)/2)) ?

The value of cos(3((3pi)/2)) is 0

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cos(3((3pi)/2))

cos (3 (\frac{3 π}{2}))

0

Solution steps

cos (3 (\frac{3 π}{2}))

= cos (3 \cdot \frac{3 π}{2})

Simplify:

3 \cdot \frac{3 π}{2} = \frac{9 π}{2}

3 \cdot \frac{3 π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 π 3}{2}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{9 π}{2}

= cos (\frac{9 π}{2})

cos (\frac{9 π}{2}) = cos (\frac{π}{2})

cos (\frac{9 π}{2})

Rewrite

\frac{9 π}{2}

2 π \cdot 2 + \frac{π}{2}

= cos (2 π 2 + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 2 + \frac{π}{2}) = cos (\frac{π}{2})

= cos (\frac{π}{2})

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

- csc (\frac{π}{2}) cot (\frac{π}{2})

- cot (\frac{2 π}{3})

- cot (π)

- cos (- \frac{π}{4})

2 sin (\frac{3}{5}) cos (\frac{4}{5})